Recovering information about a finite group from its subrack lattice


Kayacan S.

JOURNAL OF ALGEBRA, vol.582, pp.26-38, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 582
  • Publication Date: 2021
  • Doi Number: 10.1016/j.jalgebra.2021.04.026
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.26-38
  • Keywords: Subrack lattice of a group, Nilpotence class, p-Nilpotence

Abstract

We prove that the isomorphism type of the subrack lattice of a finite group determines the nilpotence class. We analyze the problem of estimating the orders of the group elements corresponding to the atoms of the subrack lattice. As a result, we show that the subrack lattice determines p-nilpotence of the group if a certain condition is met. (C) 2021 Elsevier Inc. All rights reserved.